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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
380.1.g.a	$380$	$1$	380.g	95.d	$2$	$2$	$2$	$0.190$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-19}) \)	None		✓	✓	✓	380.1.g.a	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$1$		\(q+\zeta_{6}^{2}q^{5}+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{9}+q^{11}+\cdots\)
380.1.o.a	$380$	$1$	380.o	95.h	$6$	$2$	$1$	$0.190$	\(\Q(\sqrt{-3}) \)	$D_{6}$	None	\(\Q(\sqrt{5}) \)		✓	✓	✓	380.1.o.a	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$1$		\(q-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{9}+q^{11}+\zeta_{6}^{2}q^{19}+\cdots\)
380.1.x.a	$380$	$1$	380.x	95.m	$12$	$4$	$1$	$0.190$	\(\Q(\zeta_{12})\)	$S_{4}$	None	None		✓	✓	✓	380.1.x.a	$4$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$1$		\(q+(-\zeta_{12}^{2}+\zeta_{12}^{5})q^{3}+\zeta_{12}^{2}q^{5}+\cdots\)
380.2.a.a	$380$	$2$	380.a	1.a	$1$	$1$	$1$	$3.034$	\(\Q\)	$_{}$	None	None	✓	✓	✓	✓	380.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-3q^{9}-4q^{11}-4q^{13}+\cdots\)
380.2.a.b	$380$	$2$	380.a	1.a	$1$	$1$	$1$	$3.034$	\(\Q\)	$_{}$	None	None	✓	✓	✓	✓	380.2.a.b	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+2q^{7}+q^{9}+6q^{13}+\cdots\)
380.2.a.c	$380$	$2$	380.a	1.a	$1$	$2$	$2$	$3.034$	\(\Q(\sqrt{2}) \)	$_{}$	None	None	✓	✓	✓	✓	380.2.a.c	$1$	$1$	\(0\)	\(-4\)	\(2\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{3}+q^{5}+(-2-2\beta )q^{7}+\cdots\)
380.2.a.d	$380$	$2$	380.a	1.a	$1$	$2$	$2$	$3.034$	\(\Q(\sqrt{3}) \)	$_{}$	None	None	✓	✓	✓	✓	380.2.a.d	$1$	$0$	\(0\)	\(2\)	\(2\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}+2q^{7}+(1+2\beta )q^{9}+\cdots\)
380.2.c.a	$380$	$2$	380.c	5.b	$2$	$4$	$4$	$3.034$	\(\Q(\sqrt{-2}, \sqrt{5})\)	$_{}$	None	None		✓			380.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
380.2.c.b	$380$	$2$	380.c	5.b	$2$	$6$	$6$	$3.034$	6.0.14077504.2	$_{}$	None	None		✓	✓		380.2.c.b	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{3}q^{5}+(-\beta _{3}-\beta _{4})q^{7}+\cdots\)
380.2.d.a	$380$	$2$	380.d	380.d	$2$	$16$	$16$	$3.034$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	$_{}$	\(\Q(\sqrt{-95}) \)	None		✓			380.2.d.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{11}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+\beta _{2}q^{4}-\beta _{6}q^{5}+\cdots\)
380.2.d.b	$380$	$2$	380.d	380.d	$2$	$40$	$40$	$3.034$		$_{}$	None	None		✓	✓		380.2.d.b	$8$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
380.2.f.a	$380$	$2$	380.f	76.d	$2$	$20$	$20$	$3.034$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	$_{}$	None	None		✓			380.2.f.a	$4$	$0$	\(0\)	\(0\)	\(-20\)	\(0\)		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{12}q^{2}+\beta _{10}q^{3}+\beta _{16}q^{4}-q^{5}+\cdots\)
380.2.f.b	$380$	$2$	380.f	76.d	$2$	$20$	$20$	$3.034$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	$_{}$	None	None		✓			380.2.f.b	$4$	$0$	\(0\)	\(0\)	\(20\)	\(0\)		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{15}q^{2}+\beta _{9}q^{3}-\beta _{19}q^{4}+q^{5}+\cdots\)
380.2.i.a	$380$	$2$	380.i	19.c	$3$	$2$	$1$	$3.034$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		✓			380.2.i.a	$2$	$1$	\(0\)	\(-2\)	\(1\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-4q^{7}+\cdots\)
380.2.i.b	$380$	$2$	380.i	19.c	$3$	$6$	$3$	$3.034$	6.0.1783323.2	$_{}$	None	None		✓			380.2.i.b	$2$	$0$	\(0\)	\(1\)	\(3\)	\(4\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{3}-\beta _{5})q^{3}+(1+\beta _{4})q^{5}+(1-\beta _{3}+\cdots)q^{7}+\cdots\)
380.2.i.c	$380$	$2$	380.i	19.c	$3$	$8$	$4$	$3.034$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	$_{}$	None	None		✓	✓		380.2.i.c	$2$	$0$	\(0\)	\(-1\)	\(-4\)	\(0\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{7}q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
380.2.k.a	$380$	$2$	380.k	20.e	$4$	$2$	$1$	$3.034$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		✓			380.2.k.a	$2$	$0$	\(-2\)	\(-2\)	\(-4\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i-1)q^{2}+(-i-1)q^{3}-2 i q^{4}+\cdots\)
380.2.k.b	$380$	$2$	380.k	20.e	$4$	$2$	$1$	$3.034$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		✓			380.2.k.a	$2$	$0$	\(2\)	\(2\)	\(-4\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i+1)q^{2}+(i+1)q^{3}-2 i q^{4}+\cdots\)
380.2.k.c	$380$	$2$	380.k	20.e	$4$	$52$	$26$	$3.034$		$_{}$	None	None		✓			380.2.k.c	$2$	$0$	\(-2\)	\(-2\)	\(4\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
380.2.k.d	$380$	$2$	380.k	20.e	$4$	$52$	$26$	$3.034$		$_{}$	None	None		✓			380.2.k.c	$2$	$0$	\(2\)	\(2\)	\(4\)	\(4\)			$\mathrm{SU}(2)[C_{4}]$
380.2.l.a	$380$	$2$	380.l	95.g	$4$	$8$	$4$	$3.034$	8.0.2702336256.1	$_{}$	\(\Q(\sqrt{-19}) \)	None		✓			380.2.l.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(-6\)		$2^{2}\cdot 5$	$\mathrm{U}(1)[D_{4}]$	\(q+\beta _{6}q^{5}+(-1+\beta _{3}+\beta _{5}-\beta _{6}+\beta _{7})q^{7}+\cdots\)
380.2.l.b	$380$	$2$	380.l	95.g	$4$	$12$	$6$	$3.034$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	$_{}$	None	None		✓	✓		380.2.l.b	$4$	$0$	\(0\)	\(0\)	\(4\)	\(4\)		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{3}+(\beta _{3}-\beta _{8})q^{5}+\beta _{6}q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots\)
380.2.n.a	$380$	$2$	380.n	76.f	$6$	$40$	$20$	$3.034$		$_{}$	None	None		✓			380.2.n.a	$4$	$0$	\(-3\)	\(0\)	\(20\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
380.2.n.b	$380$	$2$	380.n	76.f	$6$	$40$	$20$	$3.034$		$_{}$	None	None		✓			380.2.n.b	$4$	$0$	\(3\)	\(0\)	\(-20\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
380.2.r.a	$380$	$2$	380.r	95.i	$6$	$20$	$10$	$3.034$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	$_{}$	None	None		✓	✓	✓	380.2.r.a	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{11})q^{3}+(-\beta _{7}+\beta _{13})q^{5}+\cdots\)
380.2.s.a	$380$	$2$	380.s	380.s	$6$	$112$	$56$	$3.034$		$_{}$	None	None		✓	✓	✓	380.2.s.a	$8$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
380.2.u.a	$380$	$2$	380.u	19.e	$9$	$18$	$3$	$3.034$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	None	None		✓			380.2.u.a	$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\beta _{3}-\beta _{7})q^{3}-\beta _{4}q^{5}+(\beta _{4}-\beta _{10}+\cdots)q^{7}+\cdots\)
380.2.u.b	$380$	$2$	380.u	19.e	$9$	$18$	$3$	$3.034$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	None	None		✓			380.2.u.b	$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+\beta _{13}q^{3}+(\beta _{2}-\beta _{11})q^{5}+(-\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\)
380.2.v.a	$380$	$2$	380.v	380.v	$12$	$4$	$1$	$3.034$	\(\Q(\zeta_{12})\)	$_{}$	None	None		✓			380.2.v.a	$4$	$0$	\(-4\)	\(6\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1-\zeta_{12}^{3})q^{2}+(2-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
380.2.v.b	$380$	$2$	380.v	380.v	$12$	$4$	$1$	$3.034$	\(\Q(\zeta_{12})\)	$_{}$	None	None		✓			380.2.v.a	$4$	$0$	\(2\)	\(-6\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2+\zeta_{12}+\cdots)q^{3}+\cdots\)
380.2.v.c	$380$	$2$	380.v	380.v	$12$	$216$	$54$	$3.034$		$_{}$	None	None		✓	✓		380.2.v.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{12}]$
380.2.y.a	$380$	$2$	380.y	95.l	$12$	$4$	$1$	$3.034$	\(\Q(\zeta_{12})\)	$_{}$	None	None		✓			380.2.y.a	$4$	$0$	\(0\)	\(6\)	\(2\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\zeta_{12}+\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+(1+\cdots)q^{5}+\cdots\)
380.2.y.b	$380$	$2$	380.y	95.l	$12$	$36$	$9$	$3.034$		$_{}$	None	None		✓	✓		380.2.y.b	$4$	$0$	\(0\)	\(-6\)	\(-4\)	\(4\)			$\mathrm{SU}(2)[C_{12}]$
380.2.bb.a	$380$	$2$	380.bb	380.ab	$18$	$336$	$56$	$3.034$		$_{}$	None	None		✓	✓	✓	380.2.bb.a	$8$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
380.2.bd.a	$380$	$2$	380.bd	95.p	$18$	$60$	$10$	$3.034$		$_{}$	None	None		✓	✓	✓	380.2.bd.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
380.2.be.a	$380$	$2$	380.be	76.k	$18$	$120$	$20$	$3.034$		$_{}$	None	None		✓			380.2.be.a	$4$	$0$	\(-3\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
380.2.be.b	$380$	$2$	380.be	76.k	$18$	$120$	$20$	$3.034$		$_{}$	None	None		✓			380.2.be.b	$4$	$0$	\(3\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
380.2.bh.a	$380$	$2$	380.bh	95.r	$36$	$120$	$10$	$3.034$		$_{}$	None	None		✓	✓	✓	380.2.bh.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(6\)			$\mathrm{SU}(2)[C_{36}]$
380.2.bj.a	$380$	$2$	380.bj	380.aj	$36$	$672$	$56$	$3.034$		$_{}$	None	None		✓	✓	✓	380.2.bj.a	$8$	$0$	\(-12\)	\(0\)	\(-24\)	\(0\)			$\mathrm{SU}(2)[C_{36}]$
380.3.b.a	$380$	$3$	380.b	4.b	$2$	$72$	$72$	$10.354$		$_{}$	None	None		✓	✓	✓	380.3.b.a	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
380.3.e.a	$380$	$3$	380.e	19.b	$2$	$12$	$12$	$10.354$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	$_{}$	None	None		✓	✓	✓	380.3.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)		$2^{9}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{6}q^{5}+(-1+\beta _{6}-\beta _{11})q^{7}+\cdots\)
380.3.g.a	$380$	$3$	380.g	95.d	$2$	$4$	$4$	$10.354$	\(\Q(\sqrt{-6}, \sqrt{14})\)	$_{}$	None	None		✓			380.3.g.a	$4$	$0$	\(0\)	\(0\)	\(-20\)	\(0\)		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-5q^{5}+\beta _{2}q^{7}+5q^{9}+4q^{11}+\cdots\)
380.3.g.b	$380$	$3$	380.g	95.d	$2$	$4$	$4$	$10.354$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	$_{}$	\(\Q(\sqrt{-19}) \)	None		✓			380.3.g.b	$4$	$0$	\(0\)	\(0\)	\(9\)	\(0\)		$2^{3}\cdot 5$	$\mathrm{U}(1)[D_{2}]$	\(q+(2-\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{7}-9q^{9}+\cdots\)
380.3.g.c	$380$	$3$	380.g	95.d	$2$	$12$	$12$	$10.354$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	$_{}$	None	None		✓	✓		380.3.g.c	$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)		$2^{19}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}+(1+\beta _{3})q^{5}+\beta _{8}q^{7}+(6-\beta _{2}+\cdots)q^{9}+\cdots\)
380.3.h.a	$380$	$3$	380.h	20.d	$2$	$108$	$108$	$10.354$		$_{}$	None	None		✓	✓	✓	380.3.h.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
380.3.j.a	$380$	$3$	380.j	380.j	$4$	$232$	$116$	$10.354$		$_{}$	None	None		✓	✓	✓	380.3.j.a	$8$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
380.3.m.a	$380$	$3$	380.m	5.c	$4$	$36$	$18$	$10.354$		$_{}$	None	None		✓	✓	✓	380.3.m.a	$2$	$0$	\(0\)	\(-4\)	\(10\)	\(22\)			$\mathrm{SU}(2)[C_{4}]$
380.3.o.a	$380$	$3$	380.o	95.h	$6$	$40$	$20$	$10.354$		$_{}$	None	None		✓	✓	✓	380.3.o.a	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
380.3.p.a	$380$	$3$	380.p	380.p	$6$	$232$	$116$	$10.354$		$_{}$	None	None		✓	✓	✓	380.3.p.a	$8$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
380.3.q.a	$380$	$3$	380.q	76.g	$6$	$160$	$80$	$10.354$		$_{}$	None	None		✓	✓	✓	380.3.q.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$

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